Question
Note to moderator: “The nth Chebyshev polynomial of the first kind” is the name of a single function. The nth Chebyshev polynomial of the first kind of this function of x equals this function of n x. 64 eight-by-eight matrices span the codomain of an operation named for this function that is used in JPEG file compression. This function’s “similarity” measure equals the inner product of two vectors over the product of their magnitudes. This function of x is the (*) real part of e to the i x. This function equals the alternating sum of even-degree terms of the Maclaurin series of the exponential function. The Pythagorean theorem is a special case of a “law” named for this function in which a term vanishes because this function of 90 degrees is zero. For 10 points, name this trigonometric function equal to “adjacent over hypotenuse.” ■END■
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